Development of an active counter unmanned aerial system with integrated autonomous mobile robot for inspection and defense

Abstract

As the issue of unauthorized drone flights becomes increasingly severe, the demand for intelligent counter-drone systems is growing. Existing fixed-deployment counter-drone systems suffer from limitations such as restricted coverage and passive defense. This study proposes integrating Autonomous Mobile Robot (AMR) into the Counter-Unmanned Aerial Systems (C-UAS) architecture to develop a mobile solution with active inspection capabilities. First, a kinematic model was established to describe the mutual mapping between the motor speed and the robot speed. Second, a manual mapping method was introduced; by integrating the Extended Kalman Filter (EKF) algorithm to fuse multi-sensor data, this method enables centimeter-level positioning. Finally, the system was integrated and verified in both simulated and real-world environments. Experimental results show that the Active C-UAS can successfully navigate to the drone intrusion area while achieving high positioning accuracy, path quality, and control performance. Specifically, the Mean Absolute Error(MAE) of the actual navigation target point is only 0.35 m, and the attitude estimation error is less than 1°. Moreover, the system maintains excellent trajectory smoothness in long-distance dynamic scenarios, achieving 89.9% of the Smoothness Coefficient (SMC) benchmark from global planning while only incurring a 1.14% increase in actual path length. Finally, high control accuracy and rapid response are confirmed by an MAE below 0.02 m/s between the commanded and actual speeds, alongside a Pearson correlation coefficient () exceeding 0.9 between the two speed profiles.

Introduction

The rapid advancement of unmanned aerial vehicle (UAV) technology¹ has driven its widespread adoption across civilian and military domains², yet has simultaneously amplified associated risks³, including threats to national security, critical infrastructure, and airspace safety. In response, Counter-Unmanned Aerial Systems (C-UAS) have emerged as pivotal components of proactive airspace defense frameworks. Contemporary C-UAS solutions encompass the full operational chain of detection-localization-tracking-neutralization, with multi-modal heterogeneous data fusion techniques addressing inherent limitations of single-sensor architectures. Representative systems include the DroneSilient platform by Meghna et al.⁴, which integrates RF identification and image-capture technologies for UAV recognition, and the ADS-ZJU system developed by Shi et al.⁵, combining detection, localization, and jamming modules.

An Autonomous Mobile Robot (AMR) is defined as a robotic device capable of autonomous navigation, obstacle avoidance, and task execution in complex environments without human intervention, through its integrated sensors, control systems, and algorithms. To implement proactive anti-drone defense systems that can predict and intercept potential UAV threats in advance, while achieving dynamic collaboration between multiple C-UAS units to establish comprehensive multi-layered defense networks, it is critically necessary to equip anti-drone systems with AMR. Fig. 1 is a schematic diagram of the Active C-UAS. Under normal circumstances, the system patrols a designated area. If another device detects a drone intrusion, it will send coordinates to the system. The system will then navigate to the intrusion area via the shortest path while actively avoiding obstacles. Upon arrival, it will intercept the intruding drone. By equipping the C-UAS with autonomous mobile robots, its effective range can be expanded, environmental adaptability enhanced, and multi-system coordination improved through active patrolling, thereby better addressing the increasingly severe drone security challenges.

Fig. 1.

Active C-UAS schematic diagram.

AMR were initially designed for last-mile delivery tasks, with their technological origins tracing back to autonomous vehicles and now extending to aerial robots and mobile robotic systems. For outdoor AMR deployment, several critical challenges must be addressed, including complex terrain traversal, dynamic obstacle avoidance, and precise mapping. Although numerous studies have independently developed technologies such as localization and planning, research achievements in integrating and operationalizing these technologies remain scarce. For example, Zhu et al.⁶ proposed a robust localization model for intelligent vehicles using a Variational Bayesian (VB) approach. Ozdemir et al.⁷ developed an adaptive navigation system through Dueling Double Deep Q Networks, demonstrating competent performance in complex environments. Teng et al.⁸ introduced an adaptive LiDAR odometry and mapping framework to enable AMR applications in rugged agricultural terrains. While these contributions have advanced AMR development, current research predominantly focuses on isolated technical issues and lacks comprehensive system integration in real-world environments. To address this limitation, we have systematically integrated all system modules and rigorously validated their performance through both simulation and physical experiments.

Contribution:

1. A proactive C-UAS architecture is proposed: This study addresses the limitation of traditional fixed-deployment C-UAS by integrating AMR into the C-UAV architecture. This integration enables proactive UAV patrols, expands the coverage of the C-UAS, and enhances its flexibility.

2. Propose an EKF scheme based on manual mapping: Through manual mapping, this scheme only retains the topological structure of the road, which significantly reduces the data volume of the map. Meanwhile, it avoids the use of expensive LiDAR. Combined with EKF positioning, the scheme enables high-precision localization. In summary, this is a solution that balances low cost, low computational complexity, and high precision.

3. System integration and validation in both simulation and real-world environments: In this study, the navigation system is validated in both the Gazebo simulation environment and at three real-world locations. The experimental scenarios include narrow terrain, curved terrain, and long-distance terrain, which effectively demonstrate the feasibility of the proposed solution.

Related works

Kinematic model

The system is based on the WHEELTEC R550 PLUS omnidirectional chassis, which uses eight Mecanum wheels⁹ as the drive wheels, each controlled by an independent motor. This configuration offers advantages such as high load capacity and high flexibility, enabling the system to assist C-UAS in navigating narrow terrains and precisely adjusting heading angle. The Mecanum wheel consists of two main components: the hub and rollers. The hub serves as the main structural support, providing mounting foundations for the rollers while connecting to the robot’s drive system or chassis to transmit power and torque. The rollers are evenly distributed around the outer circumference of the hub, typically ranging from 8 to 12 in number. The axis of each roller is set at a 45°angle to the axis of the hub, which is the key structural feature enabling omnidirectional movement of the Mecanum wheels.

The control framework of the robot is shown in Fig. 2, where the red region represents the kinematic model. In the system, the Wheel Odometry is one of the multi-sensor fusion components. To obtain the Wheel Odometry, a forward kinematic model must be established, which computes the robot’s velocity based on the individual wheel speeds. Meanwhile, the output of the local planner is the robot’s velocity. To achieve control of the robot, an inverse kinematic model needs to be established, which calculates the individual wheel speeds based on the robot’s velocity.

Fig. 2.

Control framework.

The schematic diagram of the robot’s structure is shown in Fig. 3. To simplify the model, analysis is conducted only for a four-wheel Mecanum wheel robot. Before proceeding, some symbol conventions need to be established: in this study, vectors are represented by uppercase letters, while scalars are represented by lowercase letters.

Fig. 3.

The schematic diagram of the robot structure. where vectors are represented by uppercase letters and scalars by lowercase letters. The coordinate systems are defined with the origin at both the robot’s geometric center and the geometric center of the wheels. In this system, the y-axis points toward the front of the robot, and the x-axis points toward the right side of the robot.

In rigid body kinematics, the motion of a rigid body can be decomposed into two components: translation and rotation. A mobile robot can be treated as a rigid body, and its velocity V can be regarded as the superposition of the Translational Velocity and the Rotational Angular Velocity .

Rotational linear velocity refers to the linear velocity of any point on or inside the rigid body along the tangential direction of the circular path of that point when the rigid body rotates around an axis. The center of the wheel is considered to undergo circular motion with the robot’s center as the center of the circle and as the angular velocity, and the Rotational Linear Velocity follows the relationship below:

1

Where R is the direction vector from the robot’s geometric center to the wheel. The wheel speed V is composed of and :

2

Where represents the translational velocity of the robot, and is the resultant velocity of and , which is the velocity vector of a single wheel. On the other hand, the velocity can be decomposed in the xy direction, and similarly, R can also be decomposed in the xy direction. Therefore, for one wheel, the velocity components are given by:

3

Where and are the projections of and on the -axis, respectively, and their values are scalars; similarly, and are the projections of and on the -axis, respectively, and their values are also scalars. Assuming the vehicle has a length of 2a and a width of 2b, the following relationship is derived from Eqs. (1) and (3):

4

Where and are the projections of on the -axis and -axis, respectively.For the rollers, the speed is decomposed into:

5

Where and are the components of in the parallel and perpendicular directions, respectively. To obtain the projection of onto the direction of , it is sufficient to compute the dot product of and :

6

Where represents the norm of , is the unit vector in the direction of , and is the transpose of . Thus, the linear velocity is given by:

7

Where represents the rotational linear velocity of wheel 1. Based on Eq. 4, the linear velocity equation for wheel 1 can be obtained as:

8

Similarly, the equations for the other wheels can be derived as:

9

By solving Eq. (9), the forward kinematics can be obtained as:

10

It is worth noting that the speeds , , and refer to the tangential velocities at the contact points between the tires and the ground. To obtain the rotational speed of the tires, these tangential velocities need to be divided by the tire radius r to get the angular velocity in rad/s. If further conversion to the motor speed in r/min is required, the result should be multiplied by 30/π.

Localization

The localization module, as the core component of the autonomous navigation system, directly affects the vehicle’s positioning accuracy and driving safety. Global Navigation Satellite System (GNSS)¹⁰ and dead reckoning¹¹ are two key technologies for mobile robot localization. GNSS achieves absolute positioning with global coverage by analyzing satellite pseudorange observations. However, conventional GNSS systems are limited to an accuracy of about 10 meters due to multipath effects and ionospheric delays, making them insufficient for navigation requirements. Real-Time Kinematic Global Navigation Satellite System (RTK-GNSS)¹² technology improves accuracy to the centimeter level using base station differential signals. However, it heavily depends on satellite signals, leading to accuracy degradation. On the other hand, dead reckoning predicts position based on initial pose information by integrating motion state parameters. It is implemented mainly through two approaches: Wheel Odometer¹³ and Inertial Measurement Units (IMU)¹⁴. The former estimates displacement by measuring wheel speed in conjunction with a kinematic model, while the latter computes pose changes using data from gyroscopes and accelerometers. Although dead reckoning exhibits strong resistance to interference, it suffers from cumulative error effects. Wheel Odometer are prone to model deviations due to wheel slippage, while IMU-based positioning errors diverge over time due to sensor noise. Typically, high-precision estimation can only be maintained for a few minutes, requiring integration with other localization methods to achieve continuous and stable positioning.

The Extended Kalman Filter (EKF)^15,16 is an extension of the Kalman Filter (KF)^17,18 applied to nonlinear systems. This algorithm is capable of integrating information from multiple sensors and automatically adjusting the Kalman gain to achieve optimal estimation. By using EKF to fuse data from GNSS, IMU, and Wheel Odometer, the robustness of the localization process can be significantly improved.

The state equation and observation equation are as follows:

11

12

Where and represent the state vector and observation vector, respectively. and denote the dynamic model and observation model, respectively. represents the control input, while and represent the system noise and observation noise, respectively.The EKF is divided into two stages: prediction and update.

prediction:

13

14

update:

15

16

17

Where is the predicted state vector, is the predicted covariance matrix, is the process noise covariance matrix, is the Kalman gain, is the observation matrix, is the observation noise covariance matrix, is the updated state vector, and is the updated covariance matrix.

Path planning

Path planning can be categorized into global path planning and local path planning. Global path planning aims to generate a feasible path with the lowest cost based on prior global information, while local path planning focuses on generating a smooth and collision-free local path based on real-time sensor data.

Global path planning

Global path planning algorithms include grid-based methods such as the Dijkstra¹⁹ and Floyd²⁰ algorithms. These algorithms employ breadth-first search to obtain globally optimal paths; however, they are time-consuming and require re-planning when encountering obstacles. Compared to the Dijkstra algorithm, the A*²¹ algorithm considers the goal position, making it more efficient during the search process. The Jump Point Search (JPS)²² algorithm is an efficient heuristic search method for finding the shortest path on a grid map, though its preprocessing stage is computationally expensive. The Theta*²³ algorithm extends A* by detecting direct walkable paths to reduce node expansion, but it requires additional handling of diagonal obstacles, making implementation more complex. The Lifelong Planning A* (LPA*)²⁴ algorithm is an incremental heuristic search method designed for dynamic path planning but suffers from large search spaces and high memory and computational resource consumption. The D*²⁵ algorithm, a dynamic variant of A*, is well-suited for real-time path planning in dynamic environments and provides strong navigational capabilities. The D* Lite²⁶ algorithm, an incremental backward search method, reduces search space and time, thereby improving efficiency in dynamic searches. The Rapidly-exploring Random Tree (RRT)^27–29 algorithm is a probabilistic path planning method widely used in motion planning for autonomous vehicles. It is suitable for high-dimensional state spaces, unknown environments, and dynamic scenarios, but it is not ideal for applications requiring high path accuracy or optimal path solutions. Given that the A* algorithm guarantees an optimal path under certain conditions while maintaining fast convergence, this study adopts A* as the global path planning algorithm.

The A* algorithm is a heuristic search method that integrates a heuristic function and a cost function to guide the search direction. The heuristic function estimates the cost from the current node to the target node, enabling the algorithm to prioritize paths that are more likely to lead to the goal, thereby reducing search time.

The evaluation function of the A* algorithm is defined as follows:

18

Where represents the actual cost from the start node to the current node , while is the heuristic function, estimating the cost from the current node to the goal.

Algorithm 1.

A-star algorithm.

Local path planning

The classic “elastic band” approach is represented as a sequence of intermediate robot poses, denoted as . Each pose consists of the robot’s position and orientation within the given reference frame , as illustrated in Fig. 4. The sequence of these poses, referred to as a configuration, is defined as:

19

The “timed elastic band” (TEB) extends the classic elastic band by incorporating time intervals between consecutive configurations, forming a sequence of time differences :

20

Each time difference represents the duration required for the robot to transition from one configuration to the next in the sequence (Fig. 4). The TEB is formally defined as a tuple consisting of both the configuration sequence and the corresponding time intervals:

21

The core idea of TEB is to dynamically adapt and optimize both configurations and time intervals using a weighted multi-objective optimization approach in real-time:

22

where represents the optimized TEB, and is the objective function, expressed as a weighted sum of multiple components , each capturing different optimization aspects. While this represents a fundamental approach to multi-objective optimization, it already achieves excellent results.

Fig. 4.

TEB: sequences of configurations and time differences.

System implementation

Hardware development

The hardware architecture of the system is illustrated in Fig. 5. It adopts an 8-wheel omnidirectional wheel chassis as the execution unit, a Raspberry Pi as the core computing unit, and uses odometer, IMU, and RTK as the positioning sensors. Additionally, a 2D LiDAR is exclusively used for obstacle avoidance. This hardware architecture features a low-cost characteristic.

Fig. 5.

Hardware framework of the AMR.

Navigation map generation

Robot localization refers to the process of mapping a robot’s pose onto a map. Typically, outdoor robot localization relies heavily on SLAM. However, when 2D LiDAR is used for SLAM in outdoor environments, its performance is extremely poor (see Fig.6), while 3D LiDAR remains prohibitively expensive.

Fig. 6.

Navigation maps generated using a 2D LiDAR with four different SLAM algorithms. (a) Cartographer, (b) gmapping, (c) hector, (d) karto.

To address this issue, we adopted a method combining manual mapping with EKF fusion-based localization to replace SLAM. The flowchart of the manual mapping process is illustrated in Fig. 7. Compared to traditional SLAM-based dense point cloud maps, the proposed lightweight mapping approach retains only the road topology and key dimensional parameters, reducing data complexity by 2–3 orders of magnitude. This significantly alleviates the computational burden on mobile computing platforms, enhancing real-time processing efficiency.

Fig. 7.

The technical workflow of manual mapping.

Figure 8 shows the map generated by this method, which serves as the experimental site for this study. The map follows a three-level grayscale encoding scheme: black regions (grayscale value 0) represent absolute obstacle zones, white regions (grayscale value 255) denote navigable areas, and gray transition regions (grayscale value 128) indicate unclassified spaces. We conducted experiments in three different scenarios: (a) a bicycle parking area, representing a relatively narrow environment where the robot must navigate through a passage only 2 meters wide; (b) a road turning scenario, primarily designed to evaluate the robot’s turning performance; and (c) a spacious roadway, with a one-way length of 100 meters and a complete closed-loop path exceeding 200 meters, used to assess the robot’s long-distance navigation capabilities. In the figure, the left side displays photographs of the experimental sites, while the right side shows the corresponding manually mapped representations of these three scenarios.

Fig. 8.

Comparison between the real-world scene (left) and the navigation map generated using the artificial mapping method (right). (a) Map 1; (b) Map 2; (c) Map 3.

Localization methods

This study employs a multi-sensor fusion algorithm based on the EKF to enhance localization stability and accuracy. Two EKF nodes are utilized to perform global and local pose estimation, respectively, as illustrated in Fig. 9. For local pose estimation, Wheel Odometry (Odom) and IMU data are fused to generate local positioning information, while the Odom coordinate frame is transformed into the robot coordinate frame. For global pose estimation, GNSS data is first converted from the WGS-84 coordinate frame to the ENU coordinate frame. The transformed coordinates are then fused with IMU and Odom data to generate global positioning information. Finally, the transformation from the Map coordinate frame to the Odom coordinate frame is computed and transmitted.

Fig. 9.

Localization framework based on the EKF algorithm, illustrating the sensor fusion process and data flow.

The parameters for the global EKF node are shown in Table 1, which integrates data from three sensors: RTK-GNSS, Odometer, and IMU. As the robot moves solely on the ground, its motion can be regarded as two-dimensional. RTK-GNSS provides three-dimensional position information and serves as the absolute positioning data for localization. Therefore, the x and y coordinates are selected as the fusion parameters. The Wheel Odometry offers a trajectory estimate. However, due to significant errors, which affect the accuracy of the fused estimate, the three-dimensional coordinates are not fused. Nonetheless, the robot’s three-axis linear velocity derived from the kinematic model can be used for fusion. Therefore, and are chosen as the fusion parameters. The IMU, which is equipped with an EKF filter, outputs three-axis angular velocity and acceleration, as well as three-axis heading angle and linear velocity. The three-axis heading angle can be used for robot pose estimation in the fusion process. Due to model errors from the Mecanum wheels and wheel slip, the velocity calculated by the kinematic model may not be accurate. Moreover, IMU velocities derived from acceleration integration may also be inaccurate due to zero-bias instability. Thus, by using EKF to fuse the velocity parameters from Odom and IMU, more accurate data can be obtained. Consequently, the heading angle (yaw) and planar velocities and are selected as the fusion parameters.

Table 1.

Parameters of global EKF fusion configuration.

State Variables	RTK-GNSS	Odometer	IMU
Position (x, y, z)	, ,	, ,	, ,
Orientation (roll, pitch, yaw)	, ,	, ,	, ,
Linear velocity (, , )	, ,	, ,	, ,
Angular velocity (, , )	, ,	, ,	, ,
Acceleration (, , )	, ,	, ,	, ,

Navigation stack

The Framework of the navigation stack is shown in Fig. 10. After the map server node loads the pre-set Artificial Map, the navigation stack constructs a global cost map using a cost map generation algorithm. This map serves as the environmental constraint reference for global path planning. The global planner, based on the A* algorithm, generates an optimal collision-free path that connects the start point to the goal point by analyzing the passage cost matrix of the global cost map. The resolution of the path matches the map’s precision. Additionally, the EKF algorithm fuses the data from the odometer, IMU, and RTK-GNSS to generate robot positioning data. Finally, the LiDAR transmits the detected point cloud information to the navigation stack, which uses this data to generate a local cost map. The local planner, based on the TEB algorithm, plans a local path according to the grid occupancy of the local cost map and implements obstacle avoidance.

Fig. 10.

Framework of the navigation stack.

Experiments and result

This section presents the experimental results and analysis of the navigation experiments conducted with the Active C-UAS in the Gazebo simulation environment and three real-world scenarios. The experiment process involves placing the C-UAS at a starting point and then sending a target point to the C-UAS to simulate the transmission of intruding drone location information from other systems. The C-UAS then navigates to the target point. By analyzing various navigation data collected from multiple trials in different scenarios, the system’s performance in localization accuracy, path planning, and control is evaluated.

Gazebo is a powerful open-source robotics simulator that is widely used in simulation research and development in the robotics field. Fig. 11 shows the Gazebo simulation environment built for this experiment, which is constructed to scale based on the real-world environment Map 1. A differential-drive robot is used to validate the system’s performance. Figure 8 presents the three real-world environments (left) and their corresponding artificial maps (right).

Fig. 11.

The Gazebo simulation environment.

Figure 12 presents the actual trajectories of the Active C-UAS during navigation experiments in different environments. In the figure, the horizontal axis represents the X direction (unit: m), and the vertical axis represents the Y direction (unit: m). The red curve indicates the trajectory, the blue dots mark the starting points, and the green pentagrams denote the target points (multiple target points are set in each environment). In the simulation environment, Map 1, and Map 2, two target points were set in each scenario, and the C-UAS successfully completed all navigation tasks without collisions. In Map3, three target points were assigned, requiring long-distance navigation with a one-way distance of 100 m and a total path length of 200 m. Additionally, Map 3 included two obstacle points. Experimental results demonstrate that the C-UAS successfully navigated to all target points while effectively avoiding obstacles. Figure 13 further presents real-world images of the C-UAS successfully reaching the drone intrusion area. The following sections will analyze localization accuracy, path quality, and control performance based on the data collected from these navigation experiments.

Fig. 12.

The actual trajectories of the C-UAS in different environments. (a) Simulation, (b) Map 1, (c) Map 2, (d) Map 3.

Fig. 13.

C-UAS successfully navigates to the UAV intrusion area image. (a) Target point 1, (b) Target point 2, (c) Target point 3.

Localization accuracy

This section focuses on analyzing the localization accuracy of the Active C-UAS. The system’s pose estimation utilizes EKF fusion of RTK-GNSS, IMU, and Odometry to enhance localization precision and robustness. Pose estimation includes both position and attitude. First, a qualitative evaluation of position and attitude errors is conducted by comparing the trajectories obtained from different localization methods. For position, the evaluation is based on the changes in the Y-axis distance and target point errors under different localization methods. For attitude, since the actual attitude cannot be obtained, additional attitude estimation experiments are carried out. These experiments assess the error between the estimated angles and measured angles.

Figure 14 compares the trajectories obtained using different localization methods. The horizontal axis represents the X direction (unit: m), and the vertical axis represents the Y direction (unit: m). The blue line (odom) represents Odometry, calculated using kinematic equations; the green line (odom_ekf) represents EKF fusion of Odometry and IMU, referred to as local localization; the black line (gnss) represents RTK-GNSS; and the red line (gnss_ekf) represents EKF fusion of RTK-GNSS, IMU, and Odometry, referred to as global localization. Firstly, the global localization (red line) and RTK-GNSS (black line) are nearly identical, but the points in the global localization are denser than those in RTK-GNSS. This indicates that global localization offers positioning accuracy similar to RTK-GNSS but with higher output rate, thanks to the EKF fusion of IMU and Odometry. This enhances the system’s ability to adapt to dynamic environments and improves task execution accuracy. Additionally, RTK-GNSS only provides latitude, longitude, and altitude (3D coordinates), but does not offer attitude information, which is why EKF fusion with other sensors is necessary. Secondly, from the shape of the trajectory, the Odometry (blue line) trajectory in all three maps shows the lowest similarity to the other trajectories, especially in the turns where the angle estimates are too large. This demonstrates that using a kinematic model for attitude estimation results in lower accuracy. Finally, the trajectory of local localization (green line) closely matches that of global localization, but it is significantly shorter. This suggests that while the fusion of IMU improves attitude estimation accuracy, it cannot contribute to position estimation. However, by combining RTK-GNSS, this limitation can be overcome.

Fig. 14.

Trajectory deviations of different localizations. (a) Map 1, (b) Map 2, (c) Map 3.

Position

Figure 15 shows the variation in Y-axis distance under different localization methods (data from the Map 3 experiment). The horizontal axis represents time, which corresponds to the runtime in ROS, measured in nanoseconds (ns), while the vertical axis represents the Y-axis distance, measured in meters. The blue, green, black, and red lines correspond to Odometry, local localization, RTK-GNSS, and global localization, respectively. From the figure, it is evident that as time progresses, the four curves show different Y-axis distances (with the red line considered as the true curve). The global localization and RTK-GNSS curves coincide, indicating that the localization estimated by EKF does not experience any degradation in accuracy. Additionally, the actual Y-axis movement was 11 meters, with local localization deviating by 3 meters and Odometry deviating by 5 meters. This shows that both Odometry and local localization have lower positioning accuracy. However, after EKF fusion, global localization maintains the high level of accuracy provided by RTK-GNSS.

Fig. 15.

Distance changes under different localization. The figure shows the distance changes along the Y-axis under different localization methods. The blue line (odom) represents Wheel Odometry, the green line (odom_ekf) represents EKF fusion of Wheel Odometry and IMU, the black line (gnss) represents RTK-GNSS, and the red line (gnss_ekf) represents EKF fusion of RTK-GNSS, IMU, and Wheel Odometry.

Table 2 presents the error data between target points and actual points in the navigation experiments. “Environment” refers to the experimental environment, which includes both simulation and real-world environments. In the real-world environments, there are three experimental environments: Map 1, Map 2, and Map 3. The “Target Points” represent the set navigation target points, given in two-dimensional coordinates (x, y), while the “Actual Point” corresponds to the actual measured coordinates (x, y) after the navigation task is completed. “Error” represents the distance error between the Target Points and Actual Point, where is the error in the x-axis direction, is the error in the y-axis direction, and d is the straight-line distance between the Target Points and Actual Point, representing the overall error. From the table, it can be observed that the errors in the simulation environment are at the centimeter level, indicating that navigation errors are very small and can be considered negligible under ideal conditions. In the real-world environments, the overall error is approximately 0.3 meters, with an average error of 0.35 meters. Compared to the simulation environment, the error level increases to the decimeter level. This change is mainly due to certain observational noise in the localization module. Nonetheless, the system’s overall average error of 0.35 meters still indicates high localization accuracy.

Table 2.

Deviations between target points and actual point in autonomous vehicle navigation. Error represents the navigation accuracy, measured in meters, with smaller values indicating higher precision.

Environments	Target points (m)		Actual point (m)		Error (m)
	x	y	x	y			d
Simulation	-2.78	-7.42	-2.74	-7.41	0.04	0.01	0.04
	-3.38	-14.59	-3.41	-14.59	0.03	0.00	0.03
Map 1	-3.00	-7.00	-2.90	-7.27	0.10	0.27	0.29
	-3.00	-14.00	-3.34	-13.99	0.34	0.01	0.34
Map 2	15.29	17.01	15.42	16.72	0.13	0.29	0.32
	0.10	18.28	-0.18	18.08	0.28	0.20	0.34
Map 3	15.00	85.00	15.14	84.98	0.14	0.02	0.14
	4.00	80.00	3.83	79.72	0.17	0.28	0.33
	0.00	0.00	-0.68	0.06	0.68	0.06	0.68

To verify the system’s performance under localization degradation conditions, the following experiment was designed. First, the degradation of RTK positioning from fixed solution to ordinary GNSS signals—caused by factors such as obstruction and network fluctuations—is defined as “localization degradation”.

Second, both an ordinary GNSS receiver and an RTK receiver were installed on the mobile robot. Since the trajectory fused from RTK, odometer, and IMU data is the most accurate, it was used as the reference trajectory. The ordinary GNSS signal was treated as the degraded signal, and the positioning result fused from GNSS, odometer, and IMU data was regarded as the “fused positioning under degradation”. A comparison was then conducted between the degraded positioning (ordinary GNSS standalone positioning) and the fused positioning.

As shown in Fig.16, after localization degradation occurs, the (degraded) trajectory deviates rapidly from the actual trajectory, with a Root Mean Square Error (RMSE) of 2.93. After fusion, the trajectory is “pulled back” to the vicinity of the reference trajectory, and the RMSE is successfully reduced to 1.67. This indicates that the proposed fusion algorithm exhibits a certain degree of robustness–it can still maintain a small localization error when facing signal degradation.

Fig. 16.

Trajectory comparison under localization degradation conditions.

Attitude

Since this system typically operates on flat terrain, attitude estimation mainly focuses on two-dimensional heading estimation for ground movement scenarios. Although the kinematic model-based wheel odometry can estimate the heading angle by integrating angular velocity, as indicated by the previous findings, its accuracy is relatively poor. This is due to the cumulative error characteristics, which limit long-term precision. Additionally, when the IMU is exposed to external accelerations (such as movement or vibrations), the accelerometer measurements may be interfered with, affecting the accuracy of attitude estimation. To address this, we use EKF to fuse the heading angle from Odometry and IMU, thereby improving the system’s attitude estimation accuracy and robustness.

To evaluate the system’s attitude estimation accuracy, an attitude estimation experiment was designed. The experimental setup is shown in Fig.17, where the robot is placed on flat ground with reference labels. The robot is then controlled to rotate counterclockwise and stop at random angles. The actual angle is measured using a digital protractor, and the measurement results are shown in Fig.18. By comparing the estimated angles with the measured angles, the heading angle accuracy is assessed.

Fig. 17.

Schematic diagram of the orientation estimation experiment.

Fig. 18.

Images from the heading angle estimation experiment, displaying the measured results from the digital protractor.

The measured and estimated angles along with their errors are shown in Table 3. The minimum error is , the maximum error is , and the Mean Absolute Error(MAE) is only . Approximately 77.8% of the samples have errors controlled within . The Mean Error (ME) is 0.37, the Mean Square Error (MSE) is 0.89, and the Root Mean Square Error (RMSE) is 0.94, all of which are less than . This indicates that the heading angle estimation is quite accurate.

Table 3.

Heading angle estimation experiment results, presenting the estimated angles, actual angles, and their corresponding errors.

Estimate angles()	Measuring angles()	Absolute error()
44	44.2	0.2
74.5	73.9	0.6
108	106.2	1.8
128	126.9	1.1
158.5	157.8	0.7
228.5	228.2	0.3
271.5	270.7	0.8
312	312.5	0.5
341	342.3	1.3

Planned path quality

This section focuses on evaluating the path quality of the C-UAS, assessed through path length and path smoothness. To evaluate the path smoothness, we introduce the Smoothness Coefficient (SMC) as the performance metric. The calculation formula for the SMC is as follows:

23

where: represents the angle of the line segment from point to i, represents the difference in angles between adjacent line segments, is the total number of path nodes. The value of SMC ranges from 0 to 1, with a value closer to 1 indicating that the path is smoother.

The path quality parameters for each scenario are shown in Table 4. In the long-distance Map 3 environment, the actual SMC maintained 89.9% of the expected SMC, with the path length only increasing by 1.14%. However, in the complex terrain of Map 1, although the SMC remained at 88.84%, the path length increased by 8.53%. Due to the significant path length increase caused by heading adjustments in Map 2, it is excluded from consideration. The experimental results indicate that the navigation system is able to maintain good path quality in long-distance environments (Map 3), but in complex terrains (Map 1), the system must sacrifice a certain degree of path length to ensure navigation success due to factors such as kinematic constraints, safety thresholds, and control deviations.

Table 4.

Smoothness and length of paths in different environments. SMC is the path smoothness, with values closer to 1 indicating smoother paths. Length refers to the path length, where “Expected” refers to the planned path quality, and “Actual” refers to the actual path quality.

Environments	Expected SMC	Actual SMC	Expected length (m)	Actual length (m)
Simulation	0.9452	0.8749	89.64	91.59
Map 1	0.9326	0.8286	90.1	97.79
Map 2	0.9741	0.7912	46.44	56.83
Map 3	0.9982	0.8991	199.98	202.26

Control performance

This section focuses on evaluating the control performance, using the MAE, RMSE, and Pearson correlation coefficient of the control and speed curves in different environments as performance metrics.

Figure 19 shows the comparison between the control speed and the actual speed, where the control speed (red line) represents the velocity control sequence generated by the local planner, and the actual speed (blue line) is obtained by collecting motor speed through the encoder and deriving the robot’s speed using kinematic equations. Fig. (a) shows the simulation results, and (b), (c), and (d) show the actual experimental results in Map 1, Map 2, and Map 3 environments, respectively. From the figures, it can be seen that the actual speed curve is generally consistent with the control speed curve, but there are some oscillations near the control speed. As shown in Table 5, except for Map 2, the average absolute error in all scenarios is below 0.02, indicating that the oscillation amplitude is small. Furthermore, in all scenarios, the correlation coefficient between the control speed curve and the actual speed curve exceeds 0.9, indicating that the system has high control precision and good speed tracking performance. The oscillations in actual speed are mainly due to two reasons: first, there may be noise during the encoder data collection process, which causes a deviation between the measured actual speed and the true value; second, during the robot’s motion, the robot body may experience vibrations, leading to unstable torque and thus causing speed control oscillations.

Fig. 19.

Comparison of control speed and actual speed curve. The blue line represents the control speed, while the red line represents the actual speed. (a) Simulation, (b) Map 1, (c) Map 2, (d) Map 3.

Table 5.

Error and Pearson correlation coefficient between control speed and actual speed in different environments.

Environments	MAE (m/s)	RMSE (m/s)	r
Simulation	0.0182	0.028	0.9076
Map 1	0.0123	0.0264	0.9739
Map 2	0.0368	0.0736	0.9648
Map 3	0.0138	0.0322	0.9269

Conclusion

This paper addresses the limitations of fixed C-UAS, such as passive defense and limited coverage range, by proposing a solution that integrates AMR into the C-UAS architecture. First, a kinematic model was established to describe the mutual mapping between the motor speed and the robot speed. On the one hand, this model enables more accurate motion execution; on the other hand, it facilitates more precise wheel odometer estimation. Second, by introducing the combination of a manual map and the Extended Kalman Filter (EKF), not only centimeter-level positioning accuracy is achieved, but also a foundation is laid for the construction of a low-cost system. Finally, the system was integrated and verified in both simulated and real-world environments. Experimental results show that the Active C-UAS can successfully navigate to the drone intrusion area while achieving high positioning accuracy, path quality, and control performance. This study provides a research framework for an active anti-drone system and offers a low-cost integration solution for other researchers.

Although the C-UAS in this study is capable of completing basic target area navigation tasks, there are still many areas for improvement. In the future, we will explore multi-C-UAS collaborative defense. Furthermore, to enhance the system’s environmental adaptability and security, we will focus on further research into obstacle avoidance control, improving its performance in avoiding dynamic obstacles and enabling it to adapt to more complex environments.

Author contributions

S.L. conceived and designed the study. K.F. and W.C. collected the data. S.L. wrote the first draft of the manuscript. L.W. and A.F. revised the original manuscript. All authors reviewed the manuscript.

Data availability

The datasets used and analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.